In many Virtual Private Network (“VPN”) systems, a VPN server is situated within a private network that is operated on behalf of a business or other entity. A client device (such as a smartphone or personal computer) executes VPN client software, and establishes a connection to the VPN server through a public network (such as the Internet) where the client device is currently. Data communicated using this connection is encrypted, and the connection is sometimes characterized as an encrypted “tunnel” through the public network. Once the connection is established, the client device can securely access resources available on the private network where the VPN server operates. Additionally, in some instances, the client device may access resources outside of the private network by way of the VPN connection into the private network; as an example, the client device may transmit/receive data to/from a publicly available web server on the Internet, with all of the traffic between the client and the web server traversing the private network via the VPN connection.